The essential problem solved by laser cannon is the transmission of power over a very great distance. Since laser light is very focused, in theory the loss of power over a great distance from the source is reduced.

It would also make a formidable weapon.

They built my ship in two weeks flat. They started with a No. 2 General Products hull, just like the one around the Institute of Knowledge ship, and the lifesystem was practically a duplicate of the Laskins', but there the resemblance ended. There were no instruments to observe neutron stars. Instead, there was a fusion motor big enough for a Jinx warliner. In my ship, which I now called Skydiver, the drive would produce thirty gees at the safety limit. There was a laser cannon big enough to punch a hole through We Made It's moon. The puppeteer wanted me to feel safe, and now I did, for I could fight and I could run. Especially I could run.

The term "laser cannon" was used earlier. In a 1962 book titled Report on Laser Design Study, we find "results of the design analysis indicate the feasibility of proceeding with the construction of a LASER cannon system at once."
Here's another quote from the Niven/Pournelle 1974 classic Mote in God's Eye:

"Captain, look," he said, and threw a plot of the local stellar region on the screen. "The intruder came from here. Whoever launched it fired a laser cannon, or a set of laser cannon - probably a whole mess of them on asteroids, with mirrors to focus them - for about forty-five years, so the intruder would have a beam to travel on. The beam and the intruder both came straight in from the Mote.

The basic idea for the laser cannon/light sail propulsion system belongs to Robert L. Forward, who published a short paper Ground-Based Lasers For Propulsion In Space in 1961. (Read a short autobiography of Robert Forward.)

Leik Myrabo of the Rensselaer Polytechnic Institute has demonstrated that ground-based lasers can be used to shoot objects into the heavens. The small model craft succeeded in reaching over 100 feet, which compares well to the first test flight of a rocket design by Robert Goddard.

Myrabo's "lightcraft" design is a reflective funnel-shaped craft that channels heat from the laser, towards the center, causing it to literally explode the air underneath it, generating lift.

The idea of using light pressure to move a spaceship was suggested by Jules Verne in his 1867 novel From the Earth to the Moon; see the entry for light pressure propulsion. The method was explicitly described by Edmond Hamilton in his 1929 short story The Comet Doom; see the entry for ship propelled by light pressure..